All categories

3 years ago

Where are the minimum and maximum values for f(x) = -2 + 4 cos x on the interval (0,21]?

Mathematics

2 answers:

Dafna11 [192]3 years ago

4 0

Answer:

Step-by-step explanation:

Maximum value is when cos x = 1

So it is -2 + 4(1) = 2.

Minimum value, when cos x = -1:

= -2 + 4(-1) = -6.

Alex_Xolod [135]3 years ago

4 0

Answer:

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

Step-by-step explanation:

So let's first look at cos(x) on interval (0,21].

How many rotations is that? Does it at least contain 1 full rotation? If it contains one full rotation that means all the values from -1 to 1 (inclusive) are tagged? If it doesn't contain a full rotation, we might have to dig a little deeper.

So we know x=0 isn't included and that's when cosine is first 1,but this doesn't mean 1 won't be hit later.

Let's figure out the number of rotations:

21/(2pi)=3.3 approximately

This means we make at least 3 rotations.

So this means we definitely will have all the values from -1 to 1 tagged (inclusive).

Now let's look at whole function.

f(x) = -2 + 4 cos x

-2+(-4) to -2+4 will be the range of the function

So the minimum is -6 and the maximum is 2.

So the min occurs when cos(x)=-1 and the max occurs when cos(x)=1.

We have a little over three rotations and remember we can't include x=0.

cos(x)=1

when x=2pi (one full rotation)

when x=4pi (two full rotations)

when x=6pi (three full rotations)

We will stop here because cosine won't be 1 again until a fourth full rotation

cos(x)=-1

when x=pi (half rotation)

When x=3pi (one + half rotation)

When x=5pi (two+half rotation)

We can't include x=7pi (three+half rotation)

because this one is actually not in the interval because 3.5 is more than 3.3 .

The maximum 2 is reached when x=2pi,4pi, and 6pi.

The minimum -6 is reached when x=pi, 3pi,and 5pi.

You might be interested in

Find the answers to these two problems. PLEASE HELP!!

AleksAgata [21]

Alternate Interior Angles are a pair of angles on the inner side of each of those two lines but on opposite sides of the transversal.

1st question

angles 6 and 7
or
angles 2 and 3

2nd question

Angles 3 and 2
or
Angles 5 and 7

6 0

2 years ago

If 12,025 was invested at 3.25% compounded monthly 3 years, how much interest will be earned

wariber [46]

Answer:

$1,229.75

Step-by-step explanation:

Lets use the compound interest formula provided to solve this:

$A=P(1+\frac{r}{n} )^{nt}$

P = initial balance

r = interest rate (decimal)

n = number of times compounded annually

t = time

First, change 3.25% into a decimal:

3.25% -> $\frac{3.25}{100}$ -> 0.0325

Since the interest is compounded monthly, we will use 12 for n. Lets plug in the values now:

$A=12,025(1+\frac{0.0325}{12})^{12(3)}$

$A=13,254.75$

Lastly, subtract A from P to get the interest earned:

$13,254.75 - 12,025 = 1,229.75$

6 0

2 years ago

a company is offering a job with a salary of $30,000 for the first year and a 5% raise each year after that. if the 5% raise con

Ber [7]

First year is 30,000.
Earn 5% raise every year.
Growth factor is 1.05 this sounds a lot like a geometric ratio.

An = A1 × r^(n-1)Sn = A1 × (1 - r^n) / (1-r)n = 40
A1 = 30,000
A40 = $30,000 * 1.05^39 = $201,142.53

S40 = A1 * (1 - 1.05^40) / (1-1.05) which becomes:
S40 = 30,000 * -6.039988712 / -.05 which becomes:
S40 = -181,199.6614 / -.05 which becomes:
S40 = $3,623,993.227

The individual yearly calculations are shown below: